Question

Identify the domain and range of the function. y=√x-4

A. Domain: x≥−4, Range: y≥0
B. Domain: x≥4, Range: y≥0
C. Domain: x≤4, Range: y≤0
D. Domain: x≥0, Range: y≥4

Answer 1

The domain of the function y=√x-4 is restricted by the square root of a non-negative number, which means that x-4 must be greater than or equal to zero. Thus, we have:

x-4 ≥ 0

x ≥ 4

Therefore, the domain of the function is x≥4.

The range of the function is determined by the output values of the function. Since the square root of any non-negative number is always non-negative, the output values of the function y=√x-4 will always be non-negative. Thus, the range of the function is y≥0.

Therefore, the correct answer is A. Domain: x≥−4, Range: y≥0.